Problem:
Sum of Unit Fractions
(click here to see the problem statement)
My Solution
. We are looking for
where
,
, and
Simplifying,
We have,
If we let
,
then
So,
Which implies that :
Which can only be true when
, so
Using the relationship
, I set up a table
So the answer to the question,
"Which of these fractions (
, where n is a positive integer) may be expressed as the sum of two different unit fractions of integers?"
appears
to be: ALL OF THEM.
where 
, 
,
and 
,
,
so 
,
I set up a table
, where n is a positive integer)
may be expressed as the sum of two different unit fractions of
integers?" appears to be: ALL OF THEM.
